Purely Goldie Extending Modules
An -module is extending if every submodule of is essential in a direct summand of . Following Clark, an -module is purely extending if every submodule of is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Baghdad
2017-03-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/219 |
| _version_ | 1818200331073355776 |
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| author | Saad A. Al-Saadi Ikbal A. Omer |
| author_facet | Saad A. Al-Saadi Ikbal A. Omer |
| author_sort | Saad A. Al-Saadi |
| collection | DOAJ |
| description |
An -module is extending if every submodule of is essential in a direct summand of . Following Clark, an -module is purely extending if every submodule of is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module is Goldie extending if, for each submodule of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module is purely Goldie extending if, for each , there is a pure submodule P of such that . Many characterizations and properties of purely Goldie extending modules are given. Also, we discuss when a direct sum of purely Goldie extending modules is purely Goldie extending and moreover we give a sufficient condition to make this property of purely Goldie extending modules is valid.
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| first_indexed | 2024-12-12T02:35:57Z |
| format | Article |
| id | doaj.art-94f5a70fcb864c5998a20cd81e5299fb |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-12-12T02:35:57Z |
| publishDate | 2017-03-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-94f5a70fcb864c5998a20cd81e5299fb2022-12-22T00:41:17ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072017-03-01282Purely Goldie Extending ModulesSaad A. Al-SaadiIkbal A. Omer An -module is extending if every submodule of is essential in a direct summand of . Following Clark, an -module is purely extending if every submodule of is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module is Goldie extending if, for each submodule of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module is purely Goldie extending if, for each , there is a pure submodule P of such that . Many characterizations and properties of purely Goldie extending modules are given. Also, we discuss when a direct sum of purely Goldie extending modules is purely Goldie extending and moreover we give a sufficient condition to make this property of purely Goldie extending modules is valid. https://jih.uobaghdad.edu.iq/index.php/j/article/view/219extending module, purely extending module, -extending module, purely Goldie extending. |
| spellingShingle | Saad A. Al-Saadi Ikbal A. Omer Purely Goldie Extending Modules Ibn Al-Haitham Journal for Pure and Applied Sciences extending module, purely extending module, -extending module, purely Goldie extending. |
| title | Purely Goldie Extending Modules |
| title_full | Purely Goldie Extending Modules |
| title_fullStr | Purely Goldie Extending Modules |
| title_full_unstemmed | Purely Goldie Extending Modules |
| title_short | Purely Goldie Extending Modules |
| title_sort | purely goldie extending modules |
| topic | extending module, purely extending module, -extending module, purely Goldie extending. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/219 |
| work_keys_str_mv | AT saadaalsaadi purelygoldieextendingmodules AT ikbalaomer purelygoldieextendingmodules |